Stochastic Algorithms for Self-consistent Calculations of Electronic Structures
Stochastic Algorithms for Self-consistent Calculations of Electronic Structures
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DOI：
10.1090/mcom/3826
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Tae-Eon Ko;Xiantao Li
中科院分区：
文献类型：
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作者：
Tae-Eon Ko;Xiantao Li
研究了电子结构自洽场计算的一种随机算法的收敛性。该算法通过将电子电荷改写为矩阵函数的迹线/对角线来制定，随后将其表示为统计平均值。用Krylov子空间逼近进一步逼近该函数。因此，每次SCF迭代只采样一个随机向量，而不必计算所有的轨道。我们考虑具有阻尼和混合的SCF迭代的常见做法。在适当的假设下，证明了当随机误差有一个几乎确定的界时，迭代在均方意义上收敛。我们还考虑了当这种假设被削弱为二阶矩条件时的情形，并在概率上证明了收敛性。
The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electron charges as a trace/diagonal of a matrix function, which is subsequently expressed as a statistical average. The function is further approximated by using a Krylov subspace approximation. As a result, each SCF iteration only samples one random vector without having to compute all the orbitals. We consider the common practice of SCF iterations with damping and mixing. We prove with appropriate assumptions that the iterations converge in the mean-square sense, when the stochastic error has an almost sure bound. We also consider the scenario when such an assumption is weakened to a second moment condition, and prove the convergence in probability.